Final answer:
Using the compound interest formula, the amount of money that will be in the account 20 years after the plan began is approximately $103,835.16.
Step-by-step explanation:
To calculate the amount of money that will be in the account 20 years after the plan began, we can use the formula for compound interest. In this case, the amount of money deposited at the end of each month is $250. The interest rate is 12% per year, compounded monthly. The time period for the savings plan is 5 years before new obligations make it impossible to continue, meaning there will be 60 deposits in total. After these 5 years, the money will remain in the plan for the next 15 years without any deposits or withdrawals.
First, let's calculate the future value of the monthly deposits. We can use the formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value of the deposits
- P is the amount of money deposited at the end of each month ($250)
- r is the annual interest rate as a decimal (0.12)
- n is the number of times that interest is compounded per year (12)
- t is the number of years (5)
Plugging in the values, we get:
FV = 250(1 + 0.12/12)^(12*5) = $19,054.83
So, the future value of the monthly deposits after 5 years is $19,054.83.
Next, let's calculate the future value of this amount over the next 15 years without deposits or withdrawals. We can use the same formula:
FV = P(1 + r/n)^(nt)
This time, P is the amount we calculated earlier ($19,054.83), r is the same annual interest rate (0.12), n is the same number of times interest is compounded per year (12), and t is the number of years (15).
Plugging in the values, we get:
FV = 19,054.83(1 + 0.12/12)^(12*15) = $103,835.16
Therefore, the amount of money that will be in the account 20 years after the plan began is approximately $103,835.16.